This multi-center prospective, randomized clinical trial will compare the radiologic procedure of transjugular intrahepatic portal-systemic shunt (TIPS) with the surgical procedure of distal splenorenal shunt (DSRS) for variceal bleeding. The health relatedness is to define the relative merits of these two treatments with respect to morbidity, mortality and cost management. The hypothesis to be tested is that TIPS will have a significantly higher rebleeding rate and incidence of encephalopathy than DSRS. Uncontrolled studies show a variceal rebleeding rate of 20 percent after TIPS compared to 5 percent after DSRS, and an encephalopathy incidence of 30 percent after TIPS compared to 14 percent after DSRS. In this study, Childs Class A and B Cirrhotic patients with variceal bleeding which cannot be managed by endoscopy will be randomized to TIPS or DSRS. It is estimated that 140 patients need to be entered and that this population can be accrued over the initial three years of this study. A minimum follow up of two years is planned to the primary end points of variceal rebleeding and hepatic encephalopathy. The secondary endpoints will be death, ascites, need for liver transplant, shunt thrombosis or stenosis, liver function, quality of life and cost. The coordinating center at the Cleveland Clinic will be responsible for data verification, data management and statistical analysis. Significant differences in primary end points are expected in 12 to 24 months. Some of the secondary end points, death and need for transplant, may require longer follow up. This should be the definitive comparing TIPS to surgical decompression of varices (DSRS).